Monthly median f0F2 and M(3000)F2 ionospheric model, MQMF2, based on the multiquadric (MQ) method of spatial interpolation and a new ionospheric index MF2 describes the monthly median f0F2 and M(3000)F2 over Europe for any UT moment, month and level of solar activity. The multiquadric method allows a surface to be drawn strictly over a given set of points unlike many other currently used ionosphere mapping methods. A non-linear dependence of f0F2 and M(3000)F2 on solar activity level (expressed by MF2 index) is used to establish local models for each ionosonde station. Observations on 28 ionosondes for f0F2 and 19 for M(3000)F2 over 10-30 years were used for model derivation. The MQMF provides better accuracy than the CCIR model in retrospective mode over Europe. Long-term f0F2 prediction with the help of MF2 index for the rising part of solar cycle 22 is shown to provide better prediction accuracy than the CCIR model based on sunspot number R12. MQMF2 is implemented as a code for PC AT-386/387 or compatible, providing tables, plots and maps.